Evaluate 2^(1/2)*2^(1/3)

$2^{\frac{1}{2}} \cdot 2^{\frac{1}{3}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{\frac{1}{2} + \frac{1}{3}}$

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2^{\frac{1}{2} \cdot \frac{3}{3} + \frac{1}{3}}$

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2^{\frac{1}{2} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{2}{2}}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$2^{\frac{3}{2 \cdot 3} + \frac{1}{3} \cdot \frac{2}{2}}$

Multiply $2$ by $3$ .

$2^{\frac{3}{6} + \frac{1}{3} \cdot \frac{2}{2}}$

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$2^{\frac{3}{6} + \frac{2}{3 \cdot 2}}$

Multiply $3$ by $2$ .

$2^{\frac{3}{6} + \frac{2}{6}}$

Combine the numerators over the common denominator.

$2^{\frac{3 + 2}{6}}$

Add $3$ and $2$ .

$2^{\frac{5}{6}}$

The result can be shown in multiple forms.

Exact Form:

$2^{\frac{5}{6}}$

Decimal Form:

$1.78179743 \dots$